Textile processing machines, and in particular two-for-one twisters, are normally so constructed that a yarn processing station, in particular a twisting spindle, is accommodated in a machine frame in a serviceable manner, since a predominant portion of maintenance and handling work is carried out at such a position. However, in a two-for-one twister, the takeup for the cross-wound twister package is located closer to the center of the machine, i.e., there is a greater distance between the vertical servicing plane and the takeup zone.